Let $$\frac{x^2}{f(a^2+7a+3)} + \frac{y^2}{f(3a+15)} = 1$$ represent an ellipse with major axis along $$y$$-axis, where $$f$$ is a strictly decreasing positive function on $$\mathbf{R}$$. If the set of all possible values of $$a$$ is $$\mathbf{R} - [\alpha, \beta]$$, then $$\alpha^2 + \beta^2$$ is equal to :

A

28

B

40

C

61

D

24